Geodesic
Global-in-time solvability of a nonlinear system of equations of a thermal–electrical model with quadratic nonlinearity
Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 2, pp. 378-390 Cet article a éte moissonné depuis la source Math-Net.Ru

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A system of equations with a quadratic nonlinearity in the electric field potential and temperature is proposed to describe the process of heating of semiconductor elements of an electrical board, with the thermal and electrical “breakdowns” possible in the course of time. For this system of equations, the existence of a classical solution not extendable in time is proved and sufficient conditions for a unique global-in-time solvability are also obtained.
Keywords: nonlinear equations of Sobolev type, blow-up, local solubility, nonlinear capacity, estimates of blow-up time. 
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M. O. Korpusov; A. Yu. Perlov; A. V. Tymoshenko; R. S. Shafir. Global-in-time solvability of a nonlinear system of equations of a thermal–electrical model with quadratic nonlinearity. Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 2, pp. 378-390. http://geodesic.mathdoc.fr/item/TMF_2023_217_2_a8/

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